Hello ^___^
Please help me! Thank you very very much!
Determine if the planes are parallel.
[x,y,z] = [1,2,2] + s[0,-1,0] + t[0,0,1]
[x,y,z] = [1,0,-3] + s[0,0,1] + t[-1,0,0]
thank you ^__^Y
Find a normal to the first plane, and a normal to the second plane.
If the two normals are scalar multiples of each other, then the planes are parallel.
or
try to find their intersection, if you can find a solution, then they are obviously not parallel
To determine if the planes are parallel, we can examine the direction vectors of the two planes. If the direction vectors are parallel, then the planes are parallel.
Let's assign the direction vectors of the two planes as follows:
Plane 1: [0, -1, 0]
Plane 2: [0, 0, 1]
To check if the direction vectors are parallel, we can calculate their cross product. If the cross product is zero or the vectors are scalar multiples of each other, then the vectors are parallel.
To find the cross product, we can use the formula:
[X, Y, Z] = [a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1]
Where [a1, a2, a3] and [b1, b2, b3] are the components of the two vectors.
Let's calculate the cross product:
[0, -1, 0] x [0, 0, 1] = [(0 * 0) - (0 * -1), (0 * 1) - (-1 * 0), (0 * 0) - (0 * -1)] = [0, 0, 0]
Since the cross product of the direction vectors is [0, 0, 0], which is the zero vector, we can conclude that the direction vectors are parallel.
Therefore, the two planes are parallel.